Logiweb aspects of lemma -(1/3)x-(1/3)x=-(2/3)x in pyk

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The predefined "pyk" aspect

define pyk of lemma -(1/3)x-(1/3)x=-(2/3)x as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode hyphen unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode hyphen unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode equal sign unicode hyphen unicode left parenthesis unicode two unicode slash unicode three unicode right parenthesis unicode small x unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma -(1/3)x-(1/3)x=-(2/3)x as text unicode start of text unicode hyphen unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode hyphen unicode left parenthesis unicode one unicode slash unicode three unicode right parenthesis unicode small x unicode equal sign unicode hyphen unicode left parenthesis unicode two unicode slash unicode three unicode right parenthesis unicode small x unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma -(1/3)x-(1/3)x=-(2/3)x as system Q infer all metavar var x end metavar indeed - 1/ 1 + 1 + 1 * metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar = - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma -(1/3)x-(1/3)x=-(2/3)x as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed lemma (1/3)x+(1/3)x=(2/3)x conclude 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqNegated modus ponens 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar conclude - 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma -x-y=-(x+y) conclude - 1/ 1 + 1 + 1 * metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar cut lemma eqTransitivity modus ponens - 1/ 1 + 1 + 1 * metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar = - 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar modus ponens - 1/ 1 + 1 + 1 * metavar var x end metavar + 1/ 1 + 1 + 1 * metavar var x end metavar = - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar conclude - 1/ 1 + 1 + 1 * metavar var x end metavar + - 1/ 1 + 1 + 1 * metavar var x end metavar = - 1 + 1 * 1/ 1 + 1 + 1 * metavar var x end metavar end quote state proof state cache var c end expand end define